Distortion of Rabi oscillations in a compact cold-atom clock

We report on experimental measurements and theoretical calculations of Rabi oscillation distortion during rubidium clock transition in a compact cold-atom clock. The distortion of the Rabi oscillations of the clock transition caused by the magnetically sensitive transitions between magnetic sublevels is related to the duration and amplitude of the microwave pulse, the density distribution of cold atoms, and the biased magnetic field inside the microwave cavity. The theoretical calculations agreed well with the experimental results. The Rabi oscillation measurements are beneficial for determining the optimal parameters of a cold-atom clock and identifying the uniformity of the microwave field inside the cavity. This measurement can be extended to the atomic fountain clock and the vapor-cell atomic clock.

Figure 1

(a) Schematic of the experimental setup. HR, highly reflective mirror; PBS, polarizing beam splitter; PD, photodetector; QWP, quarter-wave plate. (b) Time sequence of the experiment.

Figure 2

Energy levels of the hyperfine state of the ${}^{87}\mathrm{Rb}$ atom.

Figure 3

The fitted experimental results of the atomic density distribution along the axis of the cavity.

Figure 4

The sum of atomic populations in the $|2,j\rangle$ $(j=0,\pm 1)$ states. The blue curve, dashed orange curve, and dash-dotted green curve represent durations of 0.5, 1, and 2 ms, respectively. The dotted red curve represents the atoms in the uniform microwave field.

Figure 5

The sum of atomic populations in the $|2,j\rangle$ $(j=0,\pm 1)$ states for different microwave durations. (a), (b), and (c) correspond to $\tau =0.5$, 1, and 2 ms. The blue curve illustrates the theoretical calculation, and the orange dots represent the experimental measurements.

Figure 6

Rabi oscillations between Zeeman sublevels of $|1,0\rangle \to |2,0\rangle$ (dashed orange curve), $|1,1\rangle \to |2,1\rangle$ (green curve), and $|1,-1\rangle \to |2,-1\rangle$ (dotted red curve) at $\tau =1$ ms, and their sum (dash-dotted blue curve).

Figure 7

(a) The sum of atomic populations in the $|2,j\rangle$ $(j=0,\pm 1)$ states for different biased magnetic fields ($\tau =1$ ms). The blue curve, dashed orange curve, and dash-dotted green curve represent the oscillation magnitudes under a biased magnetic field of $B_0=0.63$, 0.94, and 1.23 $\mu \mathrm{T}$, respectively. The dotted red curve represents the atoms in the uniform microwave magnetic field. (b) Probability of different sublevels ($\tau =1$ ms, $B_0=1.23$ $\mu \mathrm{T}$). The orange triangles represent the experimental measurements.